This invention relates to wavefront sensors and wavefront measuring techniques, and more particularly to lateral shearing wavefront sensors and lateral shearing wavefront measuring techniques.
Wavefront sensors refer to sensors which measure interference patterns (also referred to as “interferograms”) by superimposing two (or more) wavefronts from a test surface on a detector. The wavefronts create an interferogram in which the phase differences of the two wavefronts are encoded.
In optical profilometers, on the other hand, an interferogram is generally formed by the simultaneous reflection of an illuminating wavefront from a test surface and from a different reference surface. While there are a variety of different types of optical profilometer, in at least some embodiments light from a common source is split in two beams, one directed to the reference surface while the other is directed to the test surface. These beams are then recombined and directed by an imaging component of the interferometer to a detector. In certain embodiments (e.g., in the well-known Fizeau arrangement), all optical components from the light source to the detector are common path to both the test wavefront and the reference wavefront, except for the test surface. In this way, most of the signal due to optical imperfections of the components cancel, and high precision measurements of the test surface is possible when a high precision reference surface (or one of a known shape) is used.
In contrast, in a wavefront sensor, only the wavefront for which the “shape” has to be measured is available. The “shape” of a wavefront is defined as the phase distribution of the electromagnetic wave at a defined plane, for instance, at the detector plane. What is initially missing is the coherent reference wavefront to establish a two-beam interference. In shearing interferometry, two (or more) copies of the wavefront to be measured are produced and superimposed. Shearing can be performed in a variety of ways. For example, in rotational shearing, copies of the wavefront are rotated with respect to each other. In radial shearing, copies are variably changed in size before superposition. In reversal shear, copies are reversed with respect to each other. In lateral shear, the copies are shifted laterally before being superimposed.
In general, the wavefront sensor reconstructs the original wavefront (i.e., the wavefront formed by a test object) using the phase differences measured at different locations within the beam at the detector. This task may be mathematically challenging and a solution is not necessarily guaranteed for every arrangement.
It is believed that in lateral shearing interferometry, the phase differences from two independent shear directions should be given in order to reconstruct the wavefront. For example, C. Elster et al. have shown that a transfer function of the measured spatial frequencies of a detected interferogram is zero when spatial frequency f=1/s, where s is the shear distance (see, Appl. Opt. 38, no. 23, (1999), p. 5024-5031). However, it is believed that when a wavefront is characterized using a set of Zernike coefficients, no such restriction for the spatial frequencies is imposed as long as two orthogonal shear directions are used.